With the miniaturization of semiconductor devices in recent years, the reduction in wavelength of exposure light for use in photolithography has been proceeding. In the advanced technical field of transmission photolithography, ArF excimer laser light (wavelength: 193 nm) with a wavelength of 200 nm or less is used as exposure light. However, demand for further miniaturization has been increasing and such demand is difficult to satisfy only by using the ArF excimer laser light as the exposure light and thus has been dealt with by increasing NA by the use of the oblique illumination method or the like. With the increase in NA, however, the focal depth of exposure apparatuses has been decreasing. Accordingly, if a transfer mask is deformed to reduce its flatness when the transfer mask is set (chucked) in an exposure apparatus by vacuum suction or the like, the focus position may be shifted in transferring a mask pattern of the transfer mask onto a semiconductor substrate as a transfer target, thus degrading the transfer accuracy.
In view of this, it has been proposed to simulate, using the finite element method, a shape of a transparent substrate for use in a mask blank when the transparent substrate is set in an exposure apparatus, thereby estimating a flatness thereof. However, there has been a problem that although the shape of a main surface of the substrate can be estimated somewhat accurately by the simulation of the substrate shape using the finite element method, the time required for the simulation is very long.
In order to solve this problem, JP-A-2006-235321 (Patent Document 1) discloses a technique in which a flatness of a transparent substrate when it is set in an exposure apparatus is estimated by calculation through simulation in a short time and the transparent substrate with an excellent estimated flatness value is selected as a mask blank transparent substrate, thereby manufacturing a mask blank or an exposure mask (transfer mask) using the selected mask blank transparent substrate.
In the simulation described in Patent Document 1, a surface shape of the transparent substrate is first measured. Subsequently, the following three deformations are estimated. Herein, the direction of gravity is given as a Z-direction.
(1) a deflection of the transparent substrate along an X-direction (perpendicular to the Z-direction) due to gravity
(2) a warp of the transparent substrate along the X-direction with respect to a mask stage as fulcrums due to suction from the mask stage when the transparent substrate is set in an exposure apparatus
(3) a deformation of the transparent substrate in regions along a Y-direction (perpendicular to the X- and Z-directions) where the transparent substrate contacts the mask stage, due to suction from the mask stage when the transparent substrate is set in the exposure apparatus
Then, a simulation is carried out by a deflection differential equation using these estimated values and the surface shape of the transparent substrate measured in advance. From a surface shape, calculated by the simulation, of the transparent substrate when it is set in the exposure apparatus, a flatness thereof is obtained (calculated or found). When this flatness satisfies a specification, a mask blank or an exposure mask is produced from such a transparent substrate.